In conventional Bardeen-Cooper-Schrieffer superconductors, Cooper pairs of electrons of opposite spin (i.e., singlet structure) form the ground state. Equal-spin triplet pairs (ESTPs), as in superfluid ${}^3\mathrm{He}$, are of great interest for superconducting spintronics and topological superconductivity, yet remain elusive. Recently, odd-parity ESTPs were predicted to arise in (few-)monolayer superconducting ${\mathrm{NbSe}}_2$, from the noncollinearity between the out-of-plane Ising spin-orbit field (due to the lack of inversion symmetry in monolayer ${\mathrm{NbSe}}_2$) and an applied in-plane magnetic field. These ESTPs couple to the singlet order parameter at finite field. Using van der Waals tunnel junctions, we perform spectroscopy of superconducting ${\mathrm{NbSe}}_2$ flakes, of 2–25 monolayer thickness, measuring the quasiparticle density of states (DOS) as a function of applied in-plane magnetic field up to 33 T. In flakes $\lesssim 15$ monolayers thick the DOS has a single superconducting gap. In these thin samples, the magnetic field acts primarily on the spin (vs orbital) degree of freedom of the electrons, and superconductivity is further protected by the Ising field. The superconducting energy gap, extracted from our tunneling spectra, decreases as a function of the applied magnetic field. However, in bilayer ${\mathrm{NbSe}}_2$, close to the critical field (up to 30 T, much larger than the Pauli limit), superconductivity appears to be more robust than expected from Ising protection alone. Our data can be explained by the above-mentioned ESTPs.

In order to identify the mechanism responsible for the formation of charge-density waves (CDW) in cuprate superconductors, it is important to understand which aspects of the CDW’s microscopic structure are generic and which are material-dependent. Here, we show that, at the local scale probed by NMR, long-range CDW order in YBa₂Cu₃O_y is unidirectional with a commensurate period of three unit cells (λ = 3b), implying that the incommensurability found in X-ray scattering is ensured by phase slips (discommensurations). Furthermore, NMR spectra reveal a predominant oxygen character of the CDW with an out-of-phase relationship between certain lattice sites but no specific signature of a secondary CDW with λ = 6b associated with a putative pair-density wave. These results shed light on universal aspects of the cuprate CDW. In particular, its spatial profile appears to generically result from the interplay between an incommensurate tendency at long length scales, possibly related to properties of the Fermi surface, and local commensuration effects, due to electron-electron interactions or lock-in to the lattice.

Our measurements of ${}^{125}\mathrm{Te}$ NMR relaxations reveal an enhancement of electronic spin fluctuations above ${\mu }_0{H}^{*}\sim 15\mathrm{T}$, leading to their divergence in the vicinity of the metamagnetic transition at ${\mu }_0{H}_m\approx 35\mathrm{T}$, below which field-reinforced superconductivity appears when a magnetic field ($H$) is applied along the crystallographic $b$ axis. The NMR data evidence that these fluctuations are dominantly longitudinal, providing a key to understanding the peculiar superconducting phase diagram in $H\parallel b$, where such fluctuations enhance the pairing interactions.

In order to understand the nature of the two-dimensional Bose-Einstein condensed (BEC) phase in BaCuSi${}_{2}$O${}_{6}$, we performed detailed ${}^{63}$Cu and ${}^{29}$Si NMR above the critical magnetic field, ${H}_{c1}=23.4$ T. The two different alternating layers present in the system have very different local magnetizations close to ${H}_{c1}$; one is very weak, and its size and field dependence are highly sensitive to the nature of inter-layer coupling. Its precise value could only be determined by ``on-site'' ${}^{63}$Cu NMR, and the data are fully reproduced by a model of interacting hard-core bosons in which the perfect frustration associated to tetragonal symmetry is slightly lifted, leading to the conclusion that the population of the less populated layers is not fully incoherent but must be partially condensed.

We report the results from a thermopower and a Cu nuclear magnetic resonance (NMR) study of the infinite-${\mathrm{CuO}}_2$-layer electron-doped high-temperature superconducting cuprate (HTSC) ${\mathrm{Sr}}_{0.9}{\mathrm{La}}_{0.1}{\mathrm{CuO}}_2.$ We find that the temperature dependence of the thermopower, $S\left(T\right),$ is different from that observed in the hole-doped HTSC. In particular, we find that $\mathrm{dS}\left(T\right)/dT$ is positive above ∼120 K. However, we show that $S\left(T\right)\mathrm{}$ can still be described by the same model developed for the hole-doped HTSC and hence $S\left(T\right)\mathrm{}$ is not anomalous and does not imply phonon-mediated pairing as has previously been suggested. The Cu NMR data reveal a Knight shift and spin lattice relaxation rate below $T_c$ that are inconsistent with isotropic s-wave pairing. The Cu spin lattice relaxation rate in the normal state, however, is Curie-Weiss like and is comparable to that of the optimally and overdoped hole-doped HTSC ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4.$ The magnitude of the Knight shift indicates that the density of states at the Fermi level is anomalously small when compared with the hole-doped HTSC with the same $T_c,$ indicating that the size of ${N(E}_f)$ is of little importance in the HTSC. We find no evidence of the normal state pseudogap that is observed in the hole-doped HTSC and which was recently reported to exist in the electron-doped HTSC ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$ from infrared reflectance measurements.

Classical and quantum phase transitions (QPTs), with their accompanying concepts of criticality and universality, are a cornerstone of statistical thermodynamics. An excellent example of a controlled QPT is the field-induced ordering of a gapped quantum magnet. Although numerous “quasi-one-dimensional” coupled spin-chain and -ladder materials are known whose ordering transition is three-dimensional (3D), quasi-two-dimensional (2D) systems are special for multiple reasons. Motivated by the ancient pigment Han purple (${\mathrm{BaCuSi}}_2{\mathrm{O}}_6$), a quasi-2D material displaying anomalous critical properties, we present a complete analysis of ${\mathrm{Ba}}_{0.9}{\mathrm{Sr}}_{0.1}{\mathrm{CuSi}}_2{\mathrm{O}}_6$. We measure the zero-field magnetic excitations by neutron spectroscopy and deduce the spin Hamiltonian. We probe the field-induced transition by combining magnetization, specific-heat, torque, and magnetocalorimetric measurements with nuclear magnetic resonance studies near the QPT. With a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Sr substitution in Han purple.